Davis led the majors with 47 home runs in 2015 and has 159 homers over the past four seasons, more than any other player on the free-agent market.
If Baltimore signs Davis, it would be the biggest deal in Orioles history. The Orioles won't wait, however. They want Davis, and they want an answer from him.
Davis' agent, Scott Boras, acknowledged later Wednesday that he has "had many discussions with the Orioles."
"I don't draw lines in the sand," Boras said. "My job is to take information, and, unless Chris directs me to, you usually try to keep the doors open for everyone to listen and advance what they want to advance.
"I think when you put time frames on this, it really prevents the new idea that sometimes put deals together."
When asked whether he could confirm the seven-year, $150 million offer, Boras described the report as "inaccurate."
Davis was second in the American League in RBIs with 117 this season. He also led the majors in strikeouts with 208. Despite being prone to slumps at the plate, Davis has been valued for his prodigious power. A lefty slugger, he is the only player in the past five seasons to hit at least 50 home runs in a season, blasting 53 for the O's in 2013.
Davis' play has been instrumental in the best run in the Orioles' recent history, but a suspension for testing positive for what he said was Adderall marred the end of his 2014 season and kept him out of the team's playoff run, which ended with a loss in the ALCS.
Davis, who turns 30 in March, has also played at third base and right field since coming to Baltimore before the 2011 season.
Information from ESPN's Eddie Matz was used in this report.